There are a number of solutions that have been posted regarding how to save QuickTime movies from a browser. Some of these solutions require a trip to Terminal, or to your web browser's cache, and are somewhat cryptic to those who aren't command-line savvy. I am providing another solution that may be easier, and does not require the Terminal. This solution works with any web browser, on any OS platform.

To successfully copy a QuickTime movie using this method, you will need a text editor such as TextWrangler -- it's free, and a great text utility to have. (TextEdit will also work.) This method of copying a QuickTime movie works for movies that are kiosk-mode protected. Kiosk mode is an option that can be set for a QuickTime movie, so that even users who have QuickTime Professional cannot copy the source of a movie. Remember, this method assumes you are using QuickTime Professional.

In essence, this solution involves making a copy of a source web page containing a kiosk-protected QuickTime movie, then altering the kiosk tags so that they allow the source of the movie to be saved.

Here are the steps:

Browse to the web page that contains the QuickTime movie you want to save, and make sure the movie is fully loaded into the browser cache. You may see a light gray progress bar that shows in the QuickTime controller at the bottom of the movie showing you how much of the source movie has been downloaded to your computer. When the movie is cached (when the progress bar is gone), you have a complete copy of the movie on your local machine.

Choose View Source from the appropriate menu in your browser of choice. In Safari, this is under View -> View Source. In Firefox, it's under View -> Page Source.

You now need to save the source code of the web page to a separate file. In Safari this can be done by choosing File -> Save As... In Firefox, File -> Save Page As.... Save the file with whatever default name shows up. The name of the file doesn't matter, but it needs to have the .html file extension. Once the source of the page has been saved, you can close the source file view window.

Open the source file you just saved in a text editor. Note: Do not quit your browser, and keep the window containing the source movie open. You need to keep the browser window open so the cached movie file will not be deleted.

Search for the tags that contain NAME="kioskmode" VALUE="true". You will be changing these tags so they become NAME="kioskmode" VALUE="false".
This will disable the kiosk mode protection, and allow the source QuickTime movie to be saved. The easiest way to find all of the kiosk tags is by using Find, or Search and Replace.

In some cases, the page will contain JavaScript code that writes the QuickTime plug-in parameters to change the Kiosk mode. Searching for all of the kiosk tags will reveal all instances of code that involve kiosk. For instance, if you see something like 'kioskmode', 'true', change the word true to false.

Once you have changed all of the kiosk tags, you need to save the file. It's fine to overwrite the original with the edited version.

Open the edited file in your web browser, in a separate window. Remember, you want to keep the original window open so the movie stays in the cache.

You should now have the option to save the QuickTime video (assuming, again, that you have QuickTime Pro). Enjoy!

If you use OmniWeb as your web browser, you can skip steps number 3, 4 and 6 (and the last paragraph of step 5). The reason for this is that the page source can be edited directly within the source viewer. When you are done editing, there is a button in the toolbar that redisplays the modified page. You never have to save it as a separate file.

You could paste the source into the Snippet Editor (found in the Debug menu), but unfortunately the find dialog doesn't have the ability to replace.
Using the services menu might be a better way to go, where I have options for TextEdit, TextWrangler, and Smultron to open a new document containing the currently selected text.

HazKid - your site is valuable for those not using safari - but if you are using safari - you can copy the URL of the .mov file, and then bring up the Downloads window (command-option-L) in safari and paste (command-v) the download should begin if the link is valid.

You can also use this bookmarklet to alert the names of all the Quicktime files on the page, so that you can select the url in the alert box, copy it, and paste it into your download window.
javascript:allEmbeds=document.getElementsByTagName("embed");for(i=0;i<allEmbeds.length;i++){alert(allEmbeds[i].src)}

If the URL of the QuickTime is plainly visible in the source of the page already, all you need to do is locate it, copy/paste it into the address bar, and hit Option-Return. This will download the file to your default location.

The /problem/ comes when the URL of the file is NOT plainly visible in the source (like if the page uses javascript or something), which I can't tell if this hint covers or not, not having such a page to test it on.

To all the posters who noted that you can just paste the address into the URL box or Downloads window: you then have to RE-download the whole movie. This is not an acceptable solution for large movies (especially if they're 50+MB). If the movie is already in your cache, it's a waste of your bandwidth, disk space and time to re-download it.